To make the filling: Cut each apple quarter crosswise into ¼-inch-thick slices. Beat the eggs lightly with a fork in a small bowl, then add the milk and beat lightly again; set aside.

Melt the butter in a medium nonstick skillet over medium heat. Add the apple slices; cook, stirring occasionally, until the slices are nearly tender, about 3 minutes. Reduce the heat to medium-low; add the egg mixture. As it begins to set, use a spatula to move the cooked portion to the side, allowing the uncooked portions to spread over the bottom. (This will take about 1 minute.)

While the eggs are still very moist, reduce the heat to low; dot with the Brie and sprinkle with the chives, nutmeg, salt, and pepper. Fold some of the cooked eggs over the brie so it will melt. Remove the pan from the heat before the eggs become either dry or browned on the edges. Taste and adjust the seasoning.

Spoon half of the cooked egg mixture over the spinach on each croissant half. Top with the other half of the croissant. Serve hot, with forks.